This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and coherently combine the received multipath components of the transmitted symbols in the delay-Doppler grid using maximal ratio combining (MRC) to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in simple vector form by placing guard null symbols or zero padding (ZP) in the delay-Doppler grid and exploiting the resulting circulant property of the blocks of the channel matrix. Using this vector input-output relation we propose a low complexity iterative decision feedback equalizer (DFE) based on MRC. The performance and complexity of the proposed detector favorably compares with the state of the art message passing detector. An alternative time domain MRC based detector is also proposed for even faster detection. We further propose a Gauss-Seidel based over-relaxation parameter in the rake detector to improve the performance and the convergence speed of the iterative detection. We also show how the MRC detector can be combined with outer error-correcting codes to operate as a turbo DFE scheme to further improve the error performance. All results are compared with a baseline orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer.

Low Complexity Iterative Rake Decision Feedback Equalizer for Zero-Padded OTFS systems

Orthogonal time frequency space (OTFS) modulation has superior performance than traditional orthogonal frequency division multiplexing (OFDM) in fast time-varying scenarios. However, due to the effect of Doppler shift, higher pilot overhead and pilot power are required to estimate the channel state information. According to the sparseness of the channel in the delay-Doppler domain, this letter proposes a new pilot pattern and a sparse Bayesian learning (SBL)-based channel estimation algorithm. There is no guard pilot in the pilot pattern, and the pilot has the same power as the data. Based on the new pilot pattern, we first convert the channel estimation problem to a sparse signal recovery problem. Then, we introduce a sparse Bayesian learning framework and construct a sparse signal prior model as a hierarchical Laplace prior. Finally, the expected maximum (EM) algorithm is used to update the parameters in the prior model. Numerical simulation highlights the superiority of the proposed algorithm in terms of pilot overhead, pilot power consumption, and anti-noise interference.

Sparse Bayesian Learning of Delay-Doppler Channel for OTFS System

Rate-Splitting Multiple Access (RSMA) has emerged as a powerful multiple access, interference management, and multi-user strategy for next generation communication systems. In this tutorial, we depart from the orthogonal multiple access (OMA) versus non-orthogonal multiple access (NOMA) discussion held in 5G, and the conventional multi-user linear precoding approach used in space-division multiple access (SDMA), multi-user and massive MIMO in 4G and 5G, and show how multi-user communications and multiple access design for 6G and beyond should be intimately related to the fundamental problem of interference management. We start from foundational principles of interference management and rate-splitting, and progressively delineate RSMA frameworks for downlink, uplink, and multi-cell networks. We show that, in contrast to past generations of multiple access techniques (OMA, NOMA, SDMA), RSMA offers numerous benefits: 1) enhanced spectral, energy and computation efficiency; 2) universality by unifying and generalizing OMA, SDMA, NOMA, physical-layer multicasting, multi-user MIMO under a single framework that holds for any number of antennas at each node (SISO, SIMO, MISO, and MIMO settings); 3) flexibility by coping with any interference levels (from very weak to very strong), network loads (underloaded, overloaded), services (unicast, multicast), traffic, user deployments (channel directions and strengths); 4) robustness to inaccurate channel state information (CSI) and resilience to mixed-critical quality of service; 5) reliability under short channel codes and low latency. We then discuss how those benefits translate into numerous opportunities for RSMA in over forty different applications and scenarios of 6G, e.g., multi-user MIMO with statistical/quantized CSI, FDD/TDD/cell-free massive MIMO, millimeter wave and terahertz, cooperative relaying, physical layer security, reconfigurable intelligent surfaces, cloud-radio access network, internet-of-things, massive access, joint communication and jamming, non-orthogonal unicast and multicast, multigroup multicast, multibeam satellite, space-air-ground integrated networks, unmanned aerial vehicles, integrated sensing and communications, grant-free access, network slicing, cognitive radio, optical/visible light communications, mobile edge computing, machine/federated learning, etc. We finally address common myths and answer frequently asked questions, opening the discussions to interesting future research avenues. Supported by the numerous benefits and applications, the tutorial concludes on the underpinning role played by RSMA in next generation networks, which should inspire future research, development, and standardization of RSMA-aided communication for 6G.

A Primer on Rate-Splitting Multiple Access: Tutorial, Myths, and Frequently Asked Questions

In this paper, we investigate the impacts of transmitter and receiver windows on the performance of orthogonal time-frequency space (OTFS) modulation and propose window designs to improve the OTFS channel estimation and data detection performance. In particular, assuming ideal pulse shaping filters at the transceiver, we derive the impacts of windowing on the effective channel and its estimation performance in the delay-Doppler (DD) domain, the total average transmit power, and the effective noise covariance matrix. When the channel state information (CSI) is available at the transceiver, we analyze the minimum squared error (MSE) of data detection and propose an optimal transmitter window to minimize the detection MSE. The proposed optimal transmitter window can be interpreted as a mercury/water-filling power allocation scheme, where the mercury is firstly filled before pouring water to pre-equalize the time-frequency (TF) domain channels. When the CSI is not available at the transmitter but can be estimated at the receiver, we propose to apply a Dolph-Chebyshev (DC) window at either the transmitter or the receiver, which can effectively enhance the sparsity of the effective channel in the DD domain. Thanks to the enhanced DD domain channel sparsity, the channel spread due to the fractional Doppler is significantly reduced, which leads to a lower error floor in both channel estimation and data detection compared with that of rectangular window. Simulation results verify the accuracy of the obtained analytical results and confirm the superiority of the proposed window designs in improving the channel estimation and data detection performance over the conventional rectangular window design.

Transmitter and Receiver Window Designs for Orthogonal Time-Frequency Space Modulation

The orthogonal-time-frequency-space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To harvest the time and frequency diversity promised by OTFS, some promising detectors, especially message passing based ones, have been developed by taking advantage of the sparsity of the channel in the delay-Doppler domain. However, when the number of channel paths is relatively large or fractional Doppler shifts have to be considered, the complexity of existing detectors is a concern, and the existing message passing based detectors suffer from performance loss. In this work, we investigate the design of OTFS detectors based on the approximate message passing (AMP). In particular, leveraging the unitary AMP (UAMP), we design new detectors that enjoy the structure of the channel matrix and allow efficient implementation. In addition, the estimation of noise variance is incorporated into the UAMP-based detectors. Thanks to the robustness of UAMP relative to AMP, the UAMP-based detectors deliver superior performance, and outperform state-of-the-art detectors significantly. We also investigate iterative joint detection and decoding in a coded OTFS system, where the OTFS detectors are integrated into a powerful turbo receiver, leading to considerable performance gains. 

/pdf/iterative-detection-for-orthogonal-time-frequency-space-4t920ncz.pdf

Iterative Detection for Orthogonal Time Frequency Space Modulation With Unitary Approximate Message Passing

This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme that places information symbols in the delay-sequency domain followed by a cascade of time-division multiplexing (TDM) and Walsh-Hadamard sequence multiplexing. Thanks to the Walsh Hadamard transform (WHT), the modulation and demodulation do not require complex domain multiplications. For the proposed OTSM, we first derive the input-output relation in the delay-sequency domain and present a low complexity detection method taking advantage of zero-padding. We demonstrate via simulations that OTSM offers high performance gains over orthogonal frequency division multiplexing (OFDM) and similar performance to orthogonal time frequency space (OTFS), but at lower complexity owing to WHT. Then we propose a low complexity time-domain channel estimation method. Finally, we show how to include an outer error control code and a turbo decoder to improve error performance of the coded system.

Orthogonal Time Sequency Multiplexing Modulation: Analysis and Low-Complexity Receiver Design

This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and combine the received multipath components of the transmitted symbols in the delay-Doppler grid using linear diversity combining schemes like maximal ratio combining (MRC), equal gain combining and selection combining to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in the vector form by placing some null symbols in the delay-Doppler grid thereby exploiting the block circulant property of the channel matrix. Using the new input-output relation we propose a low complexity iterative detector based on the MRC scheme. The bit error rate (BER) performance of the proposed detector will be compared with the state of the art message passing detector and orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer. We also show that the frame error rate (FER) performance of the MRC detector can be improved by employing error correcting codes operating in the form of a turbo decision feedback equalizer (DFE).

Low Complexity Iterative Rake Detector for Orthogonal Time Frequency Space Modulation

This paper presents a low complexity detector for multiple-input multiple-output (MIMO) systems based on the recently proposed orthogonal time frequency space (OTFS) modulation. In the proposed detector, the copies of the transmitted symbol-vectors received through the different diversity branches (propagation paths and receive antennas) are linearly combined using the maximum ratio combining (MRC) technique to iteratively improve the signal to interference plus noise ratio (SINR) at the output of the combiner. To alleviate the performance degradation due to spatial correlation at the receiver antennas, we present a sample-based method to estimate such correlation and find the optimized combining weights for MRC from the estimated correlation matrix. The detector performance and complexity improve over the linear minimum mean square error (LMMSE) and message passing (MP) detectors proposed in the literature for MIMO-OTFS.

pdf/low-complexity-linear-diversity-combining-detector-for-mimo-mbd7uvmqot.pdf

Low-Complexity Linear Diversity-Combining Detector for MIMO-OTFS

This paper presents a software defined radio (SDR) Design and Implementation of an orthogonal time frequency space (OTFS) modem. OTFS is a novel modulation scheme based on multiplexing information symbols over localized pulses in the delay-Doppler signal representation. Traditional OFDM modulation operates in the frequency-time domains. In contrast, OTFS modulation operates in the delay spread-Doppler plane domains, which are related to frequency and time by the symplectic Fourier transform (similar to a two-dimensional discrete Fourier transform). OTFS is shown to perform very well under the 5G usage scenarios such as high speed vehicle to vehicle communication with wide Doppler spreads, where the traditional OFDM system performance degrades. Like any other communications system, the OTFS modem is not free from receiver impairments such as DC offset and carrier frequency offset, which affects the channel estimation and hence the decoding process. We study the effects of these receiver impairments on the receiver performance from real time experiments conducted on the implemented OTFS modem in a real indoor wireless channel. We also compare the performance of OTFS modulation and OFDM modulation using the same hardware setup and environment for the real frequency selective and partially emulated doubly selective channel.

OTFS Modem SDR Implementation and Experimental Study of Receiver Impairment Effects

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